\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t46\_bilinear (TMKvMdmHBJGgKnsQtTkqLsuAUGB7tZSzypU)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v9\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v10\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_bilinear : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v2\_bilinear : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v3\_bilinear : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v4\_bilinear : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k14\_bilinear : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_vectsp10 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k13\_bilinear : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k15\_bilinear : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k11\_bilinear : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ m1\_vectsp\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v7\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(l1\_vectsp\_1~X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X2))~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v2\_bilinear~X3~X0~X1~X2){\unicdcdcdhd}((v4\_bilinear~X3~X0~X1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X2))~(u1\_struct\_0~X0)))))))){\unicdbdjdcd}(k11\_bilinear~X0~X1~X2~X3=k11\_bilinear~\\
X0~(k6\_vectsp10~X0~X1~(k13\_bilinear~X0~X1~X2~X3))~X2~(k15\_bilinear~\\
X0~X1~X2~X3)))))\end{array}
\label{hyp:ehededpfcgjgmgjgogfgbgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}\\
((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~\\
X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~\\
X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v11\_vectsp\_1~X1~X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0)))))))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}\\
((v4\_rlvect\_1~X2){\unicdcdcdhd}((v8\_vectsp\_1~X2~X0){\unicdcdcdhd}((v9\_vectsp\_1~X2~X0){\unicdcdcdhd}\\
((v10\_vectsp\_1~X2~X0){\unicdcdcdhd}((v11\_vectsp\_1~X2~X0){\unicdcdcdhd}(l1\_vectsp\_1~X2~X0)))))))))){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~\\
(u1\_struct\_0~X2))~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_bilinear~X3~X0~X1~X2){\unicdcdcdhd}\\
((v2\_bilinear~X3~X0~X1~X2){\unicdcdcdhd}((v3\_bilinear~X3~X0~X1~X2){\unicdcdcdhd}((v4\_bilinear~\\
X3~X0~X1~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X2))~(u1\_struct\_0~X0))))))))))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k15\_bilinear~X0~X1~X2~X3)){\unicdcdcdhd}((v1\_funct\_2~(k15\_bilinear~\\
X0~X1~X2~X3)~(k2\_zfmisc\_1~(u1\_struct\_0~(k6\_vectsp10~X0~X1~(k13\_bilinear~\\
X0~X1~X2~X3)))~(u1\_struct\_0~X2))~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_bilinear~\\
(k15\_bilinear~X0~X1~X2~X3)~X0~(k6\_vectsp10~X0~X1~(k13\_bilinear~X0~\\
X1~X2~X3))~X2){\unicdcdcdhd}((v2\_bilinear~(k15\_bilinear~X0~X1~X2~X3)~X0~(k6\_vectsp10~\\
X0~X1~(k13\_bilinear~X0~X1~X2~X3))~X2){\unicdcdcdhd}((v3\_bilinear~(k15\_bilinear~\\
X0~X1~X2~X3)~X0~(k6\_vectsp10~X0~X1~(k13\_bilinear~X0~X1~X2~X3))~X2){\unicdcdcdhd}(\\
v4\_bilinear~(k15\_bilinear~X0~X1~X2~X3)~X0~(k6\_vectsp10~X0~X1~(k13\_bilinear~\\
X0~X1~X2~X3))~X2))))))\end{array}
\label{hyp:ggdgedadpfcgjgmgjgogfgbgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~\\
X0))))))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0)))))))))){\unicdcdcdhd}(m1\_vectsp\_4~X2~X0~X1))){\unicdbdjdcd}((\\
\preoh v2\_struct\_0~(k6\_vectsp10~X0~X1~X2)){\unicdcdcdhd}((v13\_algstr\_0~(k6\_vectsp10~\\
X0~X1~X2)){\unicdcdcdhd}((v2\_rlvect\_1~(k6\_vectsp10~X0~X1~X2)){\unicdcdcdhd}((v3\_rlvect\_1~\\
(k6\_vectsp10~X0~X1~X2)){\unicdcdcdhd}((v4\_rlvect\_1~(k6\_vectsp10~X0~X1~X2)){\unicdcdcdhd}\\
((v7\_vectsp\_1~(k6\_vectsp10~X0~X1~X2)~X0){\unicdcdcdhd}((v8\_vectsp\_1~(k6\_vectsp10~\\
X0~X1~X2)~X0){\unicdcdcdhd}((v9\_vectsp\_1~(k6\_vectsp10~X0~X1~X2)~X0){\unicdcdcdhd}((v10\_vectsp\_1~\\
(k6\_vectsp10~X0~X1~X2)~X0){\unicdcdcdhd}((v11\_vectsp\_1~(k6\_vectsp10~X0~X1~X2)~\\
X0){\unicdcdcdhd}(l1\_vectsp\_1~(k6\_vectsp10~X0~X1~X2)~X0)))))))))))\end{array}
\label{hyp:egehpflggdpfghfgdgehdhahbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}\\
((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~\\
X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~\\
X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v11\_vectsp\_1~X1~X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0)))))))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(l1\_vectsp\_1~X2~X0)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X2))~(u1\_struct\_0~X0)){\unicdcdcdhd}((v2\_bilinear~\\
X3~X0~X1~X2){\unicdcdcdhd}((v4\_bilinear~X3~X0~X1~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X2))~\\
(u1\_struct\_0~X0))))))))))){\unicdbdjdcd}((v1\_funct\_1~(k15\_bilinear~X0~X1~\\
X2~X3)){\unicdcdcdhd}((v1\_funct\_2~(k15\_bilinear~X0~X1~X2~X3)~(k2\_zfmisc\_1~(u1\_struct\_0~\\
(k6\_vectsp10~X0~X1~(k13\_bilinear~X0~X1~X2~X3)))~(u1\_struct\_0~X2))~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}((v2\_bilinear~(k15\_bilinear~X0~X1~X2~X3)~X0~(\\
k6\_vectsp10~X0~X1~(k13\_bilinear~X0~X1~X2~X3))~X2){\unicdcdcdhd}((v4\_bilinear~\\
(k15\_bilinear~X0~X1~X2~X3)~X0~(k6\_vectsp10~X0~X1~(k13\_bilinear~X0~\\
X1~X2~X3))~X2){\unicdcdcdhd}(m1\_subset\_1~(k15\_bilinear~X0~X1~X2~X3)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k6\_vectsp10~X0~X1~(k13\_bilinear~\\
X0~X1~X2~X3)))~(u1\_struct\_0~X2))~(u1\_struct\_0~X0))))))))\end{array}
\label{hyp:egehpflgbdfdpfcgjgmgjgogfgbgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}\\
((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~\\
X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_vectsp\_1~\\
X1~X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v2\_rlvect\_1~\\
X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}((v8\_vectsp\_1~X2~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X2~X0){\unicdcdcdhd}((v10\_vectsp\_1~X2~X0){\unicdcdcdhd}((v11\_vectsp\_1~X2~\\
X0){\unicdcdcdhd}(l1\_vectsp\_1~X2~X0)))))))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X2))~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_bilinear~X3~X0~X1~X2){\unicdcdcdhd}((v3\_bilinear~X3~X0~X1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X2))~(u1\_struct\_0~X0))))))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k14\_bilinear~\\
X0~X1~X2~X3)){\unicdcdcdhd}((v7\_vectsp\_1~(k14\_bilinear~X0~X1~X2~X3)~X0){\unicdcdcdhd}(m1\_vectsp\_4~\\
(k14\_bilinear~X0~X1~X2~X3)~X0~X2)))\end{array}
\label{hyp:egehpflgbdedpfcgjgmgjgogfgbgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}\\
((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~\\
X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~\\
X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v11\_vectsp\_1~X1~X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0)))))))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(l1\_vectsp\_1~X2~X0)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X2))~(u1\_struct\_0~X0)){\unicdcdcdhd}((v2\_bilinear~\\
X3~X0~X1~X2){\unicdcdcdhd}((v4\_bilinear~X3~X0~X1~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X2))~\\
(u1\_struct\_0~X0))))))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k13\_bilinear~X0~\\
X1~X2~X3)){\unicdcdcdhd}((v7\_vectsp\_1~(k13\_bilinear~X0~X1~X2~X3)~X0){\unicdcdcdhd}(m1\_vectsp\_4~\\
(k13\_bilinear~X0~X1~X2~X3)~X0~X1)))\end{array}
\label{hyp:egehpflgbdddpfcgjgmgjgogfgbgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((\\
v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}((v8\_vectsp\_1~X2~X0){\unicdcdcdhd}((v9\_vectsp\_1~\\
X2~X0){\unicdcdcdhd}((v10\_vectsp\_1~X2~X0){\unicdcdcdhd}((v11\_vectsp\_1~X2~X0){\unicdcdcdhd}(l1\_vectsp\_1~\\
X2~X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X2))~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_bilinear~X3~X0~X1~X2){\unicdcdcdhd}((v3\_bilinear~X3~X0~X1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X2))~(u1\_struct\_0~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\preoh v2\_struct\_0~X4){\unicdcdcdhd}\\
((v7\_vectsp\_1~X4~X0){\unicdcdcdhd}(m1\_vectsp\_4~X4~X0~X2))){\unicdbdjdcd}((X4=k14\_bilinear~\\
X0~X1~X2~X3){\unicdbdjded}(u1\_struct\_0~X4=k11\_bilinear~X0~X1~X2~X3))))))\end{array}
\label{hyp:egbdjdpfcgjgmgjgogfgbgch}
\end{equation}
\begin{theorem}\label{thm:ehedgdpfcgjgmgjgogfgbgch}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}\\
((v4\_rlvect\_1~X2){\unicdcdcdhd}((v8\_vectsp\_1~X2~X0){\unicdcdcdhd}((v9\_vectsp\_1~X2~X0){\unicdcdcdhd}\\
((v10\_vectsp\_1~X2~X0){\unicdcdcdhd}((v11\_vectsp\_1~X2~X0){\unicdcdcdhd}(l1\_vectsp\_1~X2~X0)))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X2))~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_bilinear~X3~X0~X1~\\
X2){\unicdcdcdhd}((v2\_bilinear~X3~X0~X1~X2){\unicdcdcdhd}((v3\_bilinear~X3~X0~X1~X2){\unicdcdcdhd}((v4\_bilinear~\\
X3~X0~X1~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X2))~(u1\_struct\_0~X0)))))))))){\unicdbdjdcd}\\
(k14\_bilinear~X0~X1~X2~X3=k14\_bilinear~X0~(k6\_vectsp10~X0~X1~(k13\_bilinear~\\
X0~X1~X2~X3))~X2~(k15\_bilinear~X0~X1~X2~X3)))))\end{array}$$
\end{theorem}
\end{document}
